Subgroups — #26222882

Order 12032.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
3	#20246072	C₂	1	2	yes	maximal
4	#20244260	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244127	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244066	C₂	1	2	yes	maximal, complemented
7	#20243822	C₂	1	2	yes	maximal
8	#20243413	C₂	1	1	yes	maximal, characteristic
9	#20243287	C₂	1	1	yes	maximal, characteristic, complemented
10	#103×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#467	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	#15689230	—	2	4	no	—
16	C₂×#13093956	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	#15689078	—	2	4	no	—
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15689030	C₂²	1	2	yes	—
26	#15689022	—	2	2	no	—
27	#15689022	C₂²	1	2	yes	—
28	#15689016	—	2	2	no	—
29	#15689016	—	2	2	no	—
30	#15689009	—	2	2	no	—
31	#15688983	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#467	C₄	1	8	yes	complemented
40	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₄₇	C₂²	1	2	yes	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	Q₈×Dic₄₇	—	2	4	no	—
48	Q₈×Dic₄₇	—	2	4	no	—
49	#13093983	—	2	2	no	—
50	#13093983	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
57	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	#13093956	—	2	2	no	—
63	#13093956	—	2	2	no	—
64	#13093948	—	2	4	no	—
65	#13093948	—	2	4	no	—
66	#13093934	—	2	2	no	—
67	#13093934	D₄	1	4	yes	—
68	C₈×Dic₄₇	—	2	2	no	—
69	C₈×Dic₄₇	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₄₇	—	2	2	no	—
78	C₂×Q₁₆×C₄₇	—	2	2	no	—
79	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
80	C₂²×C₈×C₄₇	—	2	2	no	—
81	C₂²×C₈×C₄₇	—	2	2	no	—
82	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²⋊Q₈×C₄₇	—	2	4	no	—
86	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	#107×C₄₇	C₂×C₄	1	4	yes	—
91	#103×C₄₇	C₂×C₄	1	8	yes	—
92	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
112	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
113	Q₁₆×C₄₇	—	2	8	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	8	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₄⋊C₄×C₄₇	—	2	8	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂²⋊C₄×C₄₇	—	2	8	no	—
125	C₂²⋊Dic₄₇	—	2	4	no	—
126	C₂²⋊Dic₄₇	—	8	2	no	—
127	C₄⋊Dic₄₇	—	2	4	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	4	4	no	—
133	C₄⋊Dic₄₇	—	8	2	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	2	1	no	—
136	C₄×Dic₄₇	—	4	4	no	—
137	C₄×Dic₄₇	—	8	2	no	—
138	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
139	C₄×Dic₄₇	#41	1	2	yes	—
140	#10625329	—	2	8	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	#41	1	2	yes	—
147	C₂³×C₄₇	—	2	1	no	—
148	C₂³×C₄₇	—	2	1	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	C₄×D₄	1	2	yes	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₄₇	—	2	4	no	—
154	Q₈×C₄₇	—	2	4	no	—
155	Q₈×C₄₇	—	4	2	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	#121	1	4	yes	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	C₄×D₄	1	4	yes	—
190	C₄₇⋊C₈	—	2	2	no	—
191	C₄₇⋊C₈	—	2	2	no	—
192	#21530	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
200	C₂²×C₄₇	#532	1	1	yes	characteristic
201	C₂²×C₄₇	#577	1	2	yes	—
202	C₂²×C₄₇	#578	1	2	yes	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	4	4	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
208	C₄×C₄₇	#525	1	1	yes	characteristic
209	C₄×C₄₇	#529	1	1	yes	characteristic
210	Dic₄₇	—	2	4	no	—
211	Dic₄₇	—	4	2	no	—
212	Dic₄₇	—	8	2	no	—
213	Dic₄₇	—	8	2	no	—
214	C₂×#467	D₄₇	1	1	yes	characteristic
215	C₂×#441	—	47	1	no	—
216	C₂×#405	—	47	1	no	—
217	#2323	—	47	2	no	—
218	#1971	—	47	1	no	—
219	#1943	—	47	1	no	—
220	#1933	—	47	2	no	—
221	#1894	—	47	2	no	—
222	#1807	—	47	1	no	—
223	#1776	—	47	1	no	—
224	C₄×#103	—	47	2	no	—
225	C₂×C₄₇	—	4	2	no	—
226	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
227	C₂×C₄₇	#2950	1	1	yes	characteristic
228	C₂×C₄₇	#2952	1	1	yes	characteristic
229	C₂×C₄₇	#3063	1	2	yes	—
230	C₂×C₄₇	#3178	1	2	yes	—
231	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
232	C₂²×M₁₆	—	47	1	no	—
233	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
235	C₂×C₄×Q₈	—	47	2	no	—
236	C₂×#117	—	47	1	no	—
237	#467	Dic₄₇	1	8	yes	complemented
238	#441	—	94	4	no	—
239	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#106	—	47	1	no	—
241	C₂×#106	—	47	1	no	—
242	C₂×#103	—	47	2	no	—
243	C₂×#103	—	47	2	no	—
244	C₂×#103	C₂×D₄₇	1	2	yes	—
245	#405	—	94	4	no	—
246	C₂×#97	—	47	1	no	—
247	C₂×#97	—	47	1	no	—
248	C₂×C₄×C₈	—	47	1	no	—
249	C₂×C₄×C₈	—	47	1	no	—
250	#391	—	47	2	no	—
251	#389	—	47	2	no	—
252	#389	—	94	2	no	—
253	#388	—	94	2	no	—
254	#388	—	94	2	no	—
255	#387	—	94	2	no	—
256	#380	—	47	2	no	—
257	C₄×C₄⋊C₄	—	47	2	no	—
258	#340	—	47	2	no	—
259	#340	—	47	2	no	—
260	#340	—	47	2	no	—
261	C₄₇	#21530	1	1	yes	characteristic, complemented, Sylow
262	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
263	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂×M₁₆	—	94	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	47	1	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
275	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
279	C₄×Q₈	—	94	4	no	—
280	C₄×Q₈	—	94	4	no	—
281	#117	—	94	2	no	—
282	#117	—	94	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	47	2	no	—
285	C₂×C₄⋊C₄	—	47	2	no	—
286	C₂×C₄⋊C₄	—	47	2	no	—
287	C₂×C₄⋊C₄	—	94	2	no	—
288	C₂×C₄⋊C₄	—	94	2	no	—
289	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	47	2	no	—
292	C₂×C₂²⋊C₄	—	94	2	no	—
293	C₂×C₄²	—	47	1	no	—
294	C₂×C₄²	—	47	1	no	—
295	C₂×C₄²	—	94	2	no	—
296	C₂×C₄²	—	94	2	no	—
297	#107	C₂×Dic₄₇	1	4	yes	—
298	#106	—	94	2	no	—
299	#106	—	94	2	no	—
300	#103	—	94	4	no	—
301	#103	—	94	4	no	—
302	#103	C₂×Dic₄₇	1	8	yes	—
303	#97	—	47	4	no	—
304	#97	—	94	2	no	—
305	C₄×C₈	—	94	2	no	—
306	C₄×C₈	—	94	2	no	—
307	#95	—	94	2	no	—
308	#95	—	94	2	no	—
309	#95	—	94	2	no	—
310	#95	—	94	2	no	—
311	#95	—	94	2	no	—
312	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	47	2	no	—
326	C₂²×C₄	—	47	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
330	C₂²×C₄	#10625352	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	Q₁₆	—	2	8	no	—
334	M₁₆	—	94	8	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	47	2	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	—	94	1	no	—
343	C₂×C₈	—	94	1	no	—
344	C₂×C₈	D₄×D₄₇	1	2	yes	—
345	C₂×C₈	#10625352	1	2	yes	—
346	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
347	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	94	4	no	—
351	C₄⋊C₄	—	94	2	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₄⋊C₄	—	94	2	no	—
354	C₄⋊C₄	—	94	2	no	—
355	C₄⋊C₄	—	376	2	no	—
356	C₄⋊C₄	—	188	4	no	—
357	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	94	4	no	—
360	C₂²⋊C₄	—	376	2	no	—
361	C₄²	—	47	2	no	—
362	C₄²	—	47	2	no	—
363	C₄²	—	94	1	no	—
364	C₄²	—	94	1	no	—
365	C₄²	—	376	2	no	—
366	C₄²	—	188	4	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	D₄×Dic₄₇	1	2	yes	—
372	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	47	4	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
402	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
405	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
407	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	94	2	no	—
410	C₈	—	94	2	no	—
411	C₈	D₄×Dic₄₇	1	4	yes	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
418	C₂²	#121×D₄₇	1	1	yes	characteristic
419	C₂²	#15689668	1	1	yes	characteristic
420	C₂²	#15689930	1	2	yes	—
421	C₂²	#15689936	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	94	4	no	—
426	C₄	—	376	2	no	—
427	C₄	—	376	2	no	—
428	C₄	—	188	2	no	—
429	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
430	C₄	#41×Dic₄₇	1	1	yes	characteristic
431	C₄	#15689633	1	1	yes	characteristic
432	C₄	#15689654	1	1	yes	characteristic
433	C₂	—	4	2	no	—
434	C₂	#121×Dic₄₇	1	1	yes	characteristic
435	C₂	#20252256	1	1	yes	characteristic
436	C₂	#20252272	1	1	yes	characteristic
437	C₂	#20253078	1	2	yes	—
438	C₂	#20254059	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#467	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#467	D₄₇
hypocenter	C₄₇	#21530
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#467

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#15689230	C₂	semidirect
4. #20244260	C₂	semidirect
5. #20244127	C₂	semidirect
6. #20244066	C₂	semidirect
9. #20243287	C₂	semidirect
10. #103×Dic₄₇	C₂	semidirect
39. C₄₇×#467	C₄	semidirect
237. #467	Dic₄₇	semidirect
261. C₄₇	#21530	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15689230	2
C₂×#15689078	2
#20246072	2
#20244260	2
#20244127	2
#20244066	2
#20243822	2
#20243413	2
#20243287	2
#103×Dic₄₇	2
C₂×C₄₇×#467	2
#21530	47